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THOMAS MUDGE 

The first Horologist who successfully applied the Detached 

Lever Escapement to Watches. 

Bom 1715— Died 1791 



AN ANALYSIS 



OF THE 



LEVER ESCAPEMENT 



BY H. R. PLAYTNER. 
I I 



A LECTURE DELIVERED BEFORE THE CANADIAN WATCHMAKERS'' 
AND RETAIL JEWELERS' ASSOCIATION. 



ILLUSTRATED. 



CHICAGO: 

Hazlitt & Walker. Publishers. 

1910. 



v."* '* . - *Y> 






War Btfpt Air 0e?f * 

0C T 2 2 193 ° J 



(V 1 






THIS IS 

GOVERNMENT PROPERTY 

FOK OFFICIAL USE ONLY 

ACCOUNTED FOR IprtEWflBSflCE WITH PAR. 693 A. P 

Before entering upon our subject proper, we think it 
advisable to explain a few points, simple though they are, 
which might cause confusion to some readers. Our 
experience has shown us that as soon as we use the words 
"millimeter" and "degree," perplexity is the result. "What 
is a millimeter?" is propounded to us very often in the 
course of a year; nearly every new acquaintance is inter- 
ested in having the metric system of measurement, together 
with the fine gauges used, explained to him. 

The metric system of measurement originated at the time 
of the French Revolution, in the latter part of the 18th cen- 
tury; its divisions are decimal, just the same as the system 
of currency we use in this country. 

A meter is the ten millionth part of an arc of the meridian 
of Paris, drawn from the equator to the north pole ; as com- 
pared with the English inch there are 39tVoVo inches in a 
meter, and there are 25.4 millimeters in an inch. 

The meter is sub-divided into decimeters, centimeters 
and millimeters; 1,000 millimeters equal one meter; the 
millimeter is again divided into ioths and the ioths into 
iooths of a millimeter, which could be continued in- 
definitely. The 1^0 millimeter is equal to the ^\o 
of an inch. These are measurements with which the watch- 
maker is concerned. T ^o millimeter, written .01 mm., is 
the side shake for a balance pivot; multiply it by 2^ and 
we obtain the thickness for the spring detent of a pocket 
chronometer, which is about Yz the thickness of a human 
hair. 

The metric system, of measurement is used in all the watch 
factories of Switzerland, France, Germany, and the United 
States, and nearly all the lathe makers number their chucks 
by it, and some of them cut the leading screws on their slide 
rests to it. 



4 PREFACE. 

In any modern work on horology of value, the metric 
system is used. Skilled horologists use it on account of its 
convenience. The millimeter is a unit which can be handled 
on the small parts of a watch, whereas the inch must al- 
ways be divided on anything smaller than the plates. 

Equally as fine gauges can be and are made for the inch 
as for the metric system, and the inch is decimally divided, 
but we require another decimal point to express our meas- 
urement. 

Metric gauges can now be procured from the material 
shops ; they consist of tenth measures, verniers and microm- 
eters ; the finer ones of these come from Glashutte, and are 
the ones mentioned by Grossmann in his essay on the lever 
escapement. Any workman who has once used these in- 
struments could not be persuaded to do without them. 

No one can comprehend the geometrical principles em- 
ployed in escapements without a knowledge of angles and 
their measurements, therefore we deem it of sufficient im- 
portance to at least explain what a degree is, as we know 
for a fact, that young workmen especially, often fail to see 
how to apply it. 

Every circle, no matter how large or small it may be, 
contains 360 ; a degree is therefore the 360th part of a 
circle ; it is divided into minutes, seconds, thirds, etc. 

To measure the value of a degree of any circle, we must 
multiply the diameter of it by 3.1416, which gives us the 
circumference, and then divide it by 360. It will be seen 
that it depends on the size of that circle or its radius, as to 
the value of a degree in any actual measurement. To illus- 
trate ; a degree on the earth's circumference measures 60 
geographical miles, while measured on the circumference 
of an escape wheel 7.5 mm. in diameter, or as they would 
designate it in a material shop, No. yy 2y it would be 7.5 X 
3.1416-^360 = .0655 mm., which is equal to the breadth of 
an ordinary human hair; it is a degree in both cases, but the 
difference is very great, therefore a degree cannot be asso- 



PREFACE. 5 

ciated with any actual measurement until the radius of -the 
circle is known. Degrees are generated from the center of 
the circle, and should be thought of as to ascension or direc- 
tion and relative value. Circles contain four right angles of 
90 each. Degrees are commonly measured by means of the 
protractor, although the ordinary instruments of this kind 
leave very much to be desired. The lines can be verified by 
means of the compass, which is a good practical method. 

It may also be well to give an explanation of some of the 
terms used. 

Drop equals the amount of freedom which is allowed for 
the action of pallets and wheel. See Z, Fig. 1. 

Primitive or Geometrical Diameter. — In the ratchet tooth 
or English wheel, the primitive and real diameter are equal ; 
in the club tooth wheel it means across the locking corners 
of the teeth ; in such a wheel, therefore, the primitive is less 
than the real diameter by the height of two impulse planes. 

Lock equals the depth of locking, measured from the 
locking corner of the pallet at the moment the drop has 
occurred. 

Run equals the amount of angular motion of pallets and 
fork to the bankings after the drop has taken place. 

Total Lock equals lock plus run. 

A Tangent is a line which touches a curve, but does not 
intersect it. AC and AD, Figs. 2 and 3, are tangents to 
the primitive circle GH at the points of intersection of EB, 
AC, and GH and FB, AD and GH. 

Impulse Angle equals the angular connection of the im- 
pulse or ruby pin with the lever fork ; or in other words, of 
the balance with the escapement. 

Impulse Radius. — From the face of the impulse* jewel 
to the center of motion, which is in the balance staff, most 
writers assume the impulse angle and radius to be equal, 
and it is true that they must conform- with one another. We 
have made a radical change in the radius and one which 
does not affect the angle. We shall prove this in due time, 



6 PREFACE. 

and also that the wider the impulse pin the greater must the 
impulse radius be, although the angle will remain un- 
changed. 

Right here we wish to put in a word of advice to all young 
men, and that is to learn to draw. No one can be a thorough 
watchmaker unless he can draw, because he cannot compre- 
hend his trade unless he can do so. 

We know what it has done for us, and we have noticed 
the same* results with others, therefore we speak from per- 
sonal experience. Attend night schools and mechanic's in- 
stitutes and improve yourselves. 

The young workmen of Toronto have a great advantage 
in the Toronto Technical School, but we are sorry to see 
that out of some 600 students, only five watchmakers at- 
tended last year. We can account for the majority of them, 
so it would seem as if the young men of the trade were not 
much interested, or thought they could not apply the knowl- 
edge to be gained there. This is a great mistake; we might 
almost say that knowledge of any kind can be applied to 
horology. The young men who take up these studies, will 
see the great advantage of them later on ; one workman will 
labor intelligently and the other do blind "guess" work. 

We are now about to enter upon our subject and deem 
it well to say, we have endeavored to make it as plain as 
possible. It is a deep subject and is difficult to treat lightly; 
we will treat it in our own way, paying special attention to 
all these points which bothered us during the many years 
of painstaking study which we gave to the subject. We 
especially endeavor to point out how theory can be applied 
to practice; while we cannot expect that everyone will un- 
derstand the subject without study, we think we have made 
it comparatively easy of comprehension. 

We will give our method of drafting the escapement, 
which happens in some respects to differ from others. We 
believe in making a drawing which we can reproduce in a 
watch. 



AN ANALYSIS OF THE LEVER ESCAPEMENT. 

The lever escapement is derived from Graham's dead- 
beat escapement for clocks. Thomas Mudge was the first 
horologist who successfully applied it to watches in the 
detached form, about 1750. The locking faces of the pallets 
were arcs of circles struck from the pallet centers. Many 
improvements were made upon it until to-day it is the best 
form of escapement for a general purpose watch, and when 
made on mechanical principles is capable of producing first 
rate results. 

Our object will be to explain the whys and wherefores of 
this escapement, and we will at once begin with the number 
of teeth in the escape wheel. It is not obligatory in the 
lever, as in the verge, to have an uneven number of teeth 
in the wheel. While nearly all have 15 teeth, we might 
make them of 14 or 16; occasionally we find some 
in complicated watches of 12 teeth, and in old English 
watches, of 30, which is a clumsy arrangement, and if the 
pallets embrace only three teeth in the latter, the pallet cen- 
ter cannot be pitched on a tangent. 

Although advisable from a timing standpoint that the 
teeth in the escape wheel should divide evenly into the num- 
ber of beats made per minute in a watch with seconds hand, 
it is not, strictly speaking, necessary that it should do so, 
as an example will show. We will take an ordinary watch, 
beating 300 times per minute ; we will fit an escape wheel of 
16 teeth ; multiply this by 2, as there is a forward and then 
a return motion of the balance and consequently two beats 
for each tooth, making 16 X 2 = 32 beats for each revolu- 
tion of the escape wheel. 300 beats are made per minute ; 
divide this by the beats made on each revolution, and we 
have the number of times in which the escape wheel re- 
volves per minute, namely, 300 ~- 32 == 9.375. This num- 
ber then is the proportion existing for the teeth and pitch 

7 



8 THE LEVER ESCAPEMENT. 

diameters of the 4th wheel and escape pinion. We must 
now find a suitable number of teeth for this wheel and 
pinion. Of available pinions for a watch, the only, one 
which would answer would be one of 8 leaves, as any other 
number would give a fractional number of teeth for the 4th 
wheel, therefore 9.375 X 8 = 75 teeth in 4th wheel. Now 
as to the proof: as is well known, if we multiply the number 
of teeth contained in 4th and escape wheels also by 2, for the 
reason previously given, and divide by the leaves in the es- 
cape pinion, we get the number of beats made per minute; 
therefore i££|S-£i = 300 beats per minute. 

Pallets can be made to embrace more than three teeth, but 
would be much heavier and therefore the mechanical action 
would suffer. They can also be made to embrace fewer 
teeth, but the necessary side shake in the pivot holes would 
prove very detrimental to a total lifting angle of io°, which 
represents the angle of movement in modern watches. Some 
of the finest ones only make 8 or 9 of a movement; the 
smaller the angle the greater will the effects of defective 
workmanship be; io° is a common-sense angle and gives a 
safe escapement capable of fine results. Theoretically, if a 
timepiece could be produced in which the balance would vi- 
brate without being connected with an escapement, we would 
have reached a step nearer the goal. Practice has shown 
this to be the proper theory to work on. Hence, the 
smaller the pallet and impulse angles the less will the bal- 
ance and escapement be connected. The chronometer is 
still more highly detached than the lever. 

The pallet embracing three teeth is sound and practical, 
and when applied to a 15 tooth wheel, this arrangement of- 
fers certain geometrical and mechanical advantages in its 
construction, which we will notice in due time. 15 teeth di- 
vide evenly into 360 leaving an interval of 24 from tooth 
to tooth, which is also the angle at which the locking faces 
of the teeth are inclined from the center, which fact will 
be found convenient when we come to cut our wheel. 



THE LEVER ESCAPEMENT. 



From locking to locking on the pallet scaping over three 
teeth, the angle is 6o°, which is equal to 2*4 spaces of the 
wheel. Fig. I illustrates the lockings, spanning this arc. If 
the pallets embraced 4 teeth, the angle would be 84 ; or in 




Fig. 1. 

case of a 16 tooth wheel scaping over three teeth, the angle 
would be «fj« =56/4°. 

Pallets may be divided into two kinds, namely : equidistant 
and circular. ^.The equidistant pallet is so-called because the 
lockings are an equal distafice from the center ; sometimes 
it is also called the tangential escapement, on account of the 
unlocking taking place on the intersection of tangent AC 




with EB, and FB with AD, the tangents, \yhich is the valu- 
able feature of this form of escapement. 

AC and AD, Fig. 2, are tangents to the primitive circle 
GH. ABE and ABF are angles of 30 each, together 



IO 



THE LEVER ESCAPEMENT. 



therefore forming the angle FBE of 6o°. The locking circle 
MN is struck from the pallet center A; the interangles be- 
ing equal, consequently the pallets must be equidistant. 

The weak point of this pallet is that the lifting is not 
performed so favorably; by examining the lifting planes 
MO and NP, we see that the discharging edge, O, is closer 
to the center, A, than the discharging edge, P ; consequently 
the lifting on the engaging pallet is performed on a shorter 
lever arm than on the disengaging pallet, also any inequality 
in workmanship would prove more detrimental on the en- 
gaging than on the disengaging pallet. The equidistant pal- 
let requires fine workmanship throughout. We have pur- 




Fig. 3. 



posely shown it of a width of io°, which is the widest we 
can employ in a 15 tooth wheel, and shows the defects of 
this escapement more readily than if we had used a narrow 
pallet. A narrower pallet is advisable, as the difference in 
the discharging edges will be less, and the lifting arms 
would, therefore, not show so much difference in leverage. 
The circular pallet is sometimes appropriately called "the 
pallet with equal lifts," as the lever arms AMO and ANP, 
Fig. 3, are equal lengths. It will be noticed by examining 
the diagram, that the' pallets are bisected by the 30 lines EB 
and FB, one-half their width being placed on each side of 
these lines. In this pallet we have two locking circles, MP 



THE LEVER ESCAPEMENT. II 

for the engaging pallet, and NO for the disengaging pallet. 
The weak points in this escapement are that the unlocking 
resistance is greater on the engaging than on the disen- 
gaging pallet, and that neither of them lock on the tangents 
AC and AD, at the points of intersection with EB and FB. 
The narrower the circular pallet is made, the nearer to the 
tangent will the unlocking be performed. In neither the 
equidistant or circular pallets can the unlocking resistance 
be exactly the same on each pallet, as in the engaging pallet 
the friction takes place before AB, the line of centers, which 
is more severe than when this line has been passed, as is the 
case with the disengaging pallet ; this fact proportionately 
increases the existing defects of the circular over the equi- 
distant pallet, and vice versa, but for the same reason, the 
lifting in the equidistant is proportionately acompanied by 
more friction than in the circular. 

Both equidistant and circular pallets have their adherents ; 
the finest Swiss, French and German watches are made with 
equidistant escapements, while the majority of English and 
American watches contain the circular. In our opinion the 
English are wise in adhering to the circular form. We think 
a ratchet wheel should not be employed with equidistant 
pallets. By examining Fig. 2, we see an English pallet of 
this form. We have shown its defects in such a wide pal- 
let as the English (as we have before stated), because they 
are more readily perceived; also, on account of the shape 
of the teeth, there is danger of the discharging edge, P, 
dipping so deep into the wheel, as to make considerable drop 
necessary, or the pallets would touch on the backs of the 
teeth. In the case of the club tooth, the latter is hollowed 
out, therefore, less drop is required. We have noticed that 
theoretically, it is advantageous to make the pallets nar- 
rower than the English, both for the equidistant and circular 
escapements. There is an escapement, Fig. 4, which is 
just the opposite to the English. The entire lift is per- 
formed by the wheel, while in the case of the ratchet wheel, 



12 



THE LEVER ESCAPEMENT. 



the entire lifting angle is on the pallets ; also, the pallets 
being as narrow as they can be made, consistent with 
strength, it has the good points of both the equidistant and 
circular pallets, as the unlocking can be performed on the 
tangent and the lifting arms are of equal length. The wheel, 
however, is so much heavier as to considerably increase the 
inertia; also, we have a metal surface of quite an extent 
sliding over a thin jewel. For practical reasons, therefore, 
it has been slightly altered in form and is only used in cheap 
work, being easily made. 

We will now consider the drop, which is a clear loss of 
power, and, if excessive, is the cause of much irregularity. It 




Fig. 4. 



should be as small as possible consistent with perfect free- 
dom of action. 

In so far as angular measurements are concerned, no hard 
and fast rule can be applied to it, the larger the escape wheel 
the smaller should be the angle allowed for drop. Authori- 
ties on the subject allow iy 2 ° drop for the club and 2° for 
the ratchet tooth. It is a fact that escape wheels are not 
cut perfectly true; the teeth are apt to bend slightly from 
the action of the cutters. The truest wheel can be made of 
steel, as each tooth can be successively ground after being 
hardened and tempered. Such a wheel would require less 
drop than one of any other metal. Supposing we have a 



THE LEVER ESCAPEMENT. 1 3 

wheel with a primitive diameter of 7.5 mm., what is the 
amount of drop, allowing iy 2 ° by angular measurement? 
7.5 X 3-i4 I 6-f-36o X i-S = .0983 mm., which is sufficient; 
a hair could get between the pallet and tooth, and would not 
stop the watch. Even after allowing for imperfectly divided 
teeth, we require no greater freedom even if the wheel is 
larger. Now suppose we take a wheel \vith a primitive di- 
ameter of 8.5 mm. and find the amount of drop ; 8.5 X 3 I 4 I 6 
-f- 360 X 1-5 = -1413 mm -> ° r .1413 — .0983 = .043 mm., 
more drop than the smaller wheel, if we take the same angle. 
This is a waste of force. The angular drop should, there- 
fore, be proportioned according to the size of the wheel. 
We wish it to be understood that common sense must always 
be our guide. When the horological student once arrives 
at this standpoint, he can intelligently apply himself to his 
calling. 

The Draw. — The draw or draft angle was added to the 
pallets in order to draw the fork back against the bankings 
and the guard point from the roller whenever the safety 
action had* performed its function. 

Pallets with draw are more difficult to unlock than those 
without it, this is in the nature of a fault, but whenever 
there are two faults we must choose the less. The rate of 
the watch will suffer less on account of the recoil introduced 
than it would were the locking faces arcs of circles struck 
from the pallet center, in which case the guard point would 
often remain against the roller. The draw should be as 
light as possible consistent with safety of action; some 
writers allow 15 on the engaging and 12 on the disengag- 
ing pallet; others again allow 12 on each, which we deem 
sufficient. The draw is measured from the locking edges 
M and N, Fig. 5. The locking planes when locked are in- 
clined 12 from EB, and FB. In the case of the engaging 
pallet it inclines toward the center A. The draw is produced 
on account of MA being longer than RA, consequently, 
when power is applied to the scape tooth S, the pallet is 



14 



THE LEVER ESCAPEMENT. 



drawn into the wheel. The disengaging pallet inclines in 
the same direction but away from the center A ; the reason 
is obvious from the former explanation. Some people im- 
agine that the greater the incline on the locking edge of the 
escape teeth, the stronger the draw would be. This is not 
the case, but it is certainly necessary that the point of the 
tooth alone should touch the pallet. From this it follows 
that the angle on the teeth must be greater than on the pal- 
lets ; examine the disengaging pallet in Fig 5, as it is from 
this pallet that the inclination of the teeth must be deter- 
mined, as in the case of .the engaging pallet the motion is 
toward the line of centers AB, and therefore away from the 




tooth, which partially explains why some people advocate 
15 draw for this pallet. As illustrated in the case of the 
disengaging pallet, however, the motion is also towards the 
line of centers AB, and tozuards the tooth as well, all of 
which will be seen by the dotted circles MM2 and NN2, 
representing the paths of the pallets. It will be noticed that 
UNF and BNB are opposite and equal angles of 12 . For 
practical reasons, from a manufacturing standpoint, the 
angle on the tooth is made just twice the amount, namely 
24 ° ; we could make it a little less or a little more. If we 
made it less than 20 too great a surface would be in con- 
tact with the jewel, involving greater friction in unlocking 
and an inefficient draw, but in the case of an English lever 



THE LEVER ESCAPEMENT. 1 5 

with such an arrangement we could do with less drop, which 
advantage would be too dearly bought; or if the angle is 
made over 28 , the point or locking edge of the tooth would 
rapidly become worn in case of a brass wheel. Also in an 
English lever more drop would be required. 

The Lock. — What we have said in regard to drop also 
applies to the lock, which should be as small as possible, 
consistent with perfect safety. The greater the drop the 
deeper must be the lock; i^° is the angle generally allowed 
for the lock, but it is obvious that in a large escapement it 
can be less. 




Fig. 6. 

The Run. — The run or, as it is sometimes called, "the 
slide/' should also be as light as possible; from %° to ^° 
is sufficient. It follows then, the bankings should be as close 
together as possible, consistent with requisite freedom for 
escaping. Anything more than this increases the angular 
connection of the balance with the escapement, which di- 
rectly violates the theory under which it is constructed ; also, 
a greater amount of work will be imposed upon the balance 
to meet the increased unlocking resistance, resulting in a 
poor motion and accurate time will be out of the question. 
It will be seen that those workmen who make a practice of 
opening the banks, "to give the escapement more freedom," 
simply jump from the frying pan into the fire. The bank- 
ings should be as far removed from the pallet center as pos- 
sible, as the further away they are pitched the less run we 
require, according to angular measurement. Figure 6 illus- 



l6 THE LEVER ESCAPEMENT. 

trates this fact; the tooth S has just dropped on the engag- 
ing pallet, but the fork has not yet reached the bankings. 
At a we have i° of run, while if placed at b we would only 
have y 2 ° of run, but still the same freedom for escaping, 
and less unlocking resistance. 

The bankings should be placed towards the acting end 
of the fork as illustrated, as in case the watch "rebanks" 
there would be more strain on the lever pivots if they were 
placed at the other end of the fork. 

The Lift. — The lift is composed of the actual lift on the 
teeth and pallets and the lock and run. We will suppose 
that from drop to drop we allow io° ; if the lock is iy 2 ° 
then the actual lift by means of the inclined planes on teeth 
and pallets will be 8^°. We have seen that a small lifting 





Fig. 7. 

angle is advisable, so that the vibrations of the balance will 
be as free as possible. There are other reasons as well. Fig. 
7 shows two inclined planes ; we desire to lift the weight 2 
a distance equal to the angle at which the planes are in- 
clined ; it will be seen at a glance that we will have less fric- 
tion by employing the smaller incline, whereas with the 
larger one the motive power is employed through a greater 
distance on the object to be moved. The smaller the angle 
the more energetic will the movement be; the grinding of 
the angles and fit of the pivots, etc., also increases in im- 
portance. An actual lift of 8^ ° satisfies the conditions im- 
posed very well. We have before seen that both on ac- 
count of the unlocking and the lifting leverage of the pal- 
let arms, it would be advisable to make them narrow both 
in the equidistant and circular escapement. We will now 



THE LEVER ESCAPEMENT. 



17 



study the question from the standpoint of the lift, in so 
far as the wheel is concerned. 

It is self-evident that a narrow pallet requires a wide 
tooth, and a wide pallet a narrow or thin tooth wheel ; in the 
ratchet wheel we have a metal point passing over a jeweled 
plane. The friction is at its minimum, because there is less 
adhesion than with the club tooth, but we must emphasize 
the fact that we require a greater angle in proportion on 
the pallets in this escapement than with the narrow pallets 
and wider tooth. This seems to be a point which many do 
not thoroughly comprehend, and we would advise a close 
study of Fig. 8, which will make it perfectly clear, as we 




Fig. 8. 



show both a wide and a narrow pallet. GH, represents the 
primitive, which in this figure is also the real diameter of 
the escape wheel. In measuring the lifting angles for the 
pallets, our starting point is always from the tangents AC 
and AD. The tangents are straight lines, but the wheel de- 
scribes the circle GH, therefore they must deviate from one 
another, and the closer to the center A the discharging edge 
of the engaging pallet reaches, the greater does this differ- 
ence become ; and in the same manner the further the dis- 
charging edge of the disengaging pallet is from the center 
A the greater it is. This shows that the loss is greater in 
the equidistant than in the circular escapement. After this 



l8 THE LEVER ESCAPEMENT. 

we will designate this difference as the "loss." In order to 
illustrate it more plainly we show the widest pallet — the 
English — in equidistant form. This gives another reason 
why the English lever should only be made with circular 
pallets, as we have seen that the wider the pallet the greater 
the loss. The loss is measured at the intersection of the 
path o>f the discharging edge OO, with the circle G H, and 
is shown through AC2, which intersects these circles at that 
point. In the case of the disengaging pallet, PP illustrates 
the path of the discharging edge ; the loss is measured as 
in the preceding case where GH is intersected as shown by 
AD2. It amounts to a different value on each pallet. Notice 
the loss between C and C2, on the engaging, and D and D2 
on the disengaging pallet ; it is greater on the engaging pal- 
let, so much so that it amounts. to 2°, which is equal to the 
entire lock; therefore if 8^° of work is to be accomplished 
through this pallet, the lifting plane requires an angle of 
ioy 2 ° struck from AC. 

Let us now consider the lifting action of the club tooth 
wheel. This is decidedly a complicated action, and requires 
some study to comprehend. In action with the engaging 
pallet the wheel moves up, or in the direction of the motion 
of the pallets, but on the disengaging pallet it moves down, 
and in a direction opposite to the pallets, and the heel of the 
tooth moves with greater velocity than the locking edge; 
also in the case of the engaging pallet, the locking edge 
moves with greater velocity than the discharging edge; in 
the disengaging pallet the opposite is the case, as the dis- 
charging edge moves with greater velocity than the locking. 
These points involve factors which must be considered, and 
the drafting of a correct action is of paramount importance; 
we therefore show the lift as it is accomplished in four dif- 
ferent stages in a good action. Fig. 9 illustrates the en- 
gaging, and Fig. 10 the disengaging pallet; by comparing 
the figures it will be noticed that the lift takes place on 
the point of the tooth similar to the English, until the dis- 



THE LEVER ESCAPEMENT. 



19 



charging edge of the pallet has been passed, when the heel 
gradually comes into play on the engaging, but more quickly 
on the disengaging pallet. 

We 'will also notice that during the first part of the lift 
the tooth moves faster along the engaging lifting plane 
than on the disengaging; on pallets 2 and 3 this differ- 
ence is quite large ; towards the latter part of the lift the 
action becomes quicker on the disengaging pallet and slower 
on the engaging. 

To obviate this difficulty some fine watches, notably 
those of A. Lange & Sons, have convex lifting planes on 
the engaging and concave on the disengaging pallets ; 







Fig. 9. 



the lifting planes on the teeth are also curved. See Fig. 
11. This is decidedly an ingenious arrangement, and is 
in strict accordance with scientific investigation. We 
should see rnany fine watches made with such escape- 
ments if the means for producing them could fully satisfy 
the requirements of the scientific principles involved. 

The distribution of the lift on tooth and pallet is a very 
important matter; the lifting angle on the tooth must be 
less in proportion to its width than it is on the pallet. For 
the sake of making it perfectly plain, we illustrate what 
should not be made; if we have io^° for width of tooth 
and pallet, and take half of it for a tooth, and the other 



20 



THE LEVER ESCAPEMENT. 



half for the pallet, making each of them $}i° in width, 
and suppose we have a lifting of 8^2° to distribute between 
them, by allowing 4^° on each, the lift would take place 
as shown in Fig. 12, which is a very unfavorable action. 
The edge of the engaging pallet scrapes on the lifting 
plane of the tooth, yet it is astonishing to find some other- 
wise very fine watches being manufactured right along 
which contain this fault ; such watches can be stopped 
with the ruby pin in the fork and the engaging pallet 
in action, nor would they start when run down as soon 
as the crown is touched, no matter how well they were 
finished and fitted. 

The lever lengths of the club tooth are variable, while 
with the ratchet they are constant, which is in its favor ; 




Fig. 10. 



in the latter it would always be as SB, Fig. 13. This is 
a shorter lever than QB, consequently more powerful, al- 
though the greater velocity is at Q, which only comes 
into action after the inertia of wheel and pallets has been 
overcome, and when the greatest momentum during con- 
tact is reached. SB is the primitive radius of the club 
tooth wheel, but both primitive and real radius of the 
ratchet wheel. The distance of centers of wheel and pal- 
let will be alike in both cases ; also the lockings will be the 
same distance apart on both pallets ; therefore, when horolo- 
gists, even if they have worldwide reputations, claim that 
the club tooth has an advantage over the ratchet because 



THE LEVER ESCAPEjMENT. 



21 



it begins the lift with a shorter lever than the latter, it 
does not make it so. We are treating the subject from a 
purely horological standpoint, and neither patriotism or 
prejudice has anything to do with it. We wish to sift the 




Fig. 11. 

matter thoroughly and arrive at a just conception of the 
merits and defects of each form of escapement, and show 
reasons for our conclusions. 

Anyone who has closely followed our deductions must 
see that in so far as the wheel is concerned the ratchet 





Fig. 12. 



Fig. 13. 



or English wheel has several points in its favor. Such a 
wheel is inseparable from a wide pallet; but we have 
seen that a narrower pallet is advisable ; also as little drop 
and lock as possible ; clearly, we must effect a compromise. 



22 



THE LEVER ESCAPEMENT. 



In other words, so far the balance of our reasoning is in 
favor of the club tooth escapement and to effect an in- 
telligent division of angles for tooth, pallet and lift is one 
of the great questions which confronts the intelligent horolo- 
gist. 

Anyone who has ever taken the pains to draw pallet 
and tooth with different angles, through every stage of 
the lift, with both wide and narrow pallets and teeth, in 
circular and equidistant escapements, will have received an 
eye-opener. We strongly advise all our readers who are 
practical workmen to try it after studying what we have 
said. We are certain it will repay them. 




The Center Distance of Wheel and Pallets. The direc- 
tion of pressure of the wheel teeth should be through the 
pallet center by drawing the tangents AC and AD, Fig. 2 
to the primitive circle GH, at the intersection of the angle 
FBE. This condition is realized in the equidistant pallet. 
In the circular pallet, Fig. 3, this condition cannot exist, 
as in order to lock on a tangent the center distance should 
be greater for the engaging and less for the disengaging 
pallet, therefore watchmakers aim to go between the two 
and plant them as before specified at A. 

When planted on the tangents the unlocking resistance 
will be less and the impulse transmitted under favorable 



THE LEVER ESCAPEMENT. 



23 



conditions, especially so in the circular, as the direction of 
pressure coincides (close to the center of the lift), with 
the law of the parallelogram of forces. 

It is impossible to plant pallets on the tangents in very 
small escapements, as there would not be enough room 
for a pallet arbor of proper strength, nor will they be 
found planted on the tangents in the medium size escape- 
ment with a long pallet arbor, nor in such a one with a 
very wide tooth (see Fig. 4) as the heel would come so 
close to the center A, that the solidity of pallets and arbor 
would suffer. We w T ill give an actual example. For a 
medium sized escape wheel with a primitive diameter of 




Fig. 3. 

7.5 mm., the center distance AB is 4.33 mm. By using 
3 of a lifting angle on the teeth, the distance from the 
heel of the tooth to the pallet center will be .4691 mm. ; 
by allowing .1 mm. between wheel and pallet and .15 mm. 
for stock on the pallets we find we will have a pallet 
arbor as follows: .4691— (.1+. 15) X 2 = .4382 mm. It 
would not be practicable to make anything smaller. 

It behooves us now to see that while a narrow pallet, is 
advisable a very wide tooth is not; yet these two are in- 
separable. Here is another case for a compromise, as, 
unquestionably the pallets ought to be planted on the tan- 
gents. There is no difficulty about it in the English Jever, 



2 4 



THE LEVER ESCAPEMENT. 



and we have shown in our example that a judiciously 
planned club tooth escapement of medium size can be made 
with the center distance properly planted. 

When considering the center distance we must of ne- 
cessity consider the widths of teeth and pallets and their 
lifting angles. We are now at a point in which no watch- 
maker of intelligence would indicate one certain division 
for these parts and claim it to be "the best." It is always 
those who do not thoroughly understand a subject who 
are the first to make such claims. We will, however, 
give our opinion within certain limits. The angle to be 
divided for tooth and pallet is io^°. Let us divide it by 




Fi£. 4. 



2, which would be the most natural thing to do, and ex- 
amine the problem. We will have 5^4° each for width of 
tooth and pallet. We must have a smaller lifting angle on 
the tooth than on the pallet, but the wider the tooth the 
greater should its lifting angle be. It would not be me- 
chanical to make the tooth wide and the lifting angle 
small, as the lifting plane on the pallets would be too steep 
on account of being narrow. A lifting angle on the tooth 
which would be exactly suitable for a given circular, would 
be too great for a given equidistant pallet. It follows, 
therefore, taking 5^° as a width for the tooth, that while 
we «ould employ it in a fair sized escapement with equi- 



THE LEVER ESCAPEMENT. 2$ 

distant pallets, we could not do so with circular pallets and 
still have the latter pitched on the tangents. We see the 
majority of escapements made with narrower teeth than 
pallets, and for a very good reason. 

In the example previously given, the 3 lift on the 
tooth is well adapted for a width of 4^°, which would 
require a pallet 6° in width. The tooth, therefore, would 
be 24 the width of pallets, which is very good indeed. 

From what we have said it follows that a large num- 
ber of pallets are not planted on the tangents at all. We 
have never noticed this question in print before. Writers 
generally seem to, in fact do, assume that no matter how 
large or small the escapement may be, or how the pallets 
and teeth are divided for width and lifting angle, no diffi- 
culty will be found in locating the pallets on the tangents. 
Theoretically there is no difficulty, but in practice we find 
there is. 

Equidistant vs. Circular. At this stage we are able to 
weigh the circular against the equidistant pallet. In 
beginning this essay we had to explain the difference be- 
tween them, so the reader could follow our discussion, and 
not until now, are we able to sum up our conclusions. 

The reader will have noticed that for such an important 
action as the lift, which supplies power to the balance, the 
circular pallet is favored from every point of view. This 
is a very strong point in its favor. On the other hand, the 
unlocking resistance being less, and as nearly alike as 
possible on both pallets in the equidistant, it is a question 
if the total vibration of the balance will be greater with 
the one than the other, although it will receive the im- 
pulse under better conditions from the circular pallet; but 
it expends more force in unlocking it. Escapement fric- 
tion plays an important role in the position and isochronal 
adjustments; the greater the friction encountered the slower 
the vibration of the balance. The friction should be con- 
stant. In unlocking, the equidistant comes nearer to- ful- 



26 THE LEVER ESCAPEMENT. 

filling this condition, while during the lift it is more nearly 
so in the circular. The friction in unlocking, from a timing 
standpoint, overshadows that of the impulse, and the tooth 
can be a little wider in the equidistant than the circular 
escapement with the pallet properly planted. Therefore 
for the -finest watches the equidistant escapement is well 
adapted, but for anything less than that the circular should 
be our choice. 

The Fork and Roller Action, While the lifting action 
of the lever escapement corresponds to that of the cylin- 
der, the fork and roller action corresponds to the impulse 
action in the chronometer and duplex escapements. 

Our experience leads us to believe that the action now 
under consideration is but imperfectly understood by many 
workmen. It is a complicated action, and when out of order 
is the cause of many annoying stoppages, often character- 
ized by the watch starting when taken from the pocket. 

The action is very important and is generally divided 
into impulse and safety action, although we think we ought 
to divide it into three, namely, by adding that of the un- 
locking action. We will first of all consider the impulse 
and unlocking actions, because we cannot intelligently con- 
sider the one without the other, as the ruby pin and the 
slot in the fork are utilized in each. The ruby pin, or 
strictly speaking, the "impulse radius/' is a lever arm, whose 
length is measured from the center of the balance staff 
to the face of the ruby pin, and is used, firstly, as a power 
or transmitting lever on the acting or geometrical length 
of the fork (i. e., from the pallet center to the beginning 
of the horn), and which at the moment is a resistance lever, 
to be utilized in unlocking the pallets. After the pallets 
are unlocked the conditions are reversed, and we now find 
the lever fork, through the pallets, transmitting power to 
the balance by means of the impulse radius. In the first 
part of the action we have a short lever engaging a longer 
one, which is an advantage. See Fig. 14, where we have 



THE LEVER ESCAPEMENT. 



27 



purposely somewhat exaggerated the conditions. A' X 
represents the impulse radius at present under discussion, 
and AW the acting length of the fork. It will be seen 
that the shorter the impulse radius, or in other words, the 
closer the ruby pin is to the balance staff and the longer 
the fork, the easier will be the unlocking of the pallets be 
performed, but this entails a great impulse angle, for the 
law applicable to the case is, that the angles are in the in- 
verse ratio to the radii. In other words, the shorter the 
radius, the greater is the angle, and the smaller the angle 





ij 



,"# 



the greater is the radius. We know, though, that we must 
have as small an impulse angle as possible in order that the 
balance should be" highly detached. Here is one point in 
favor of a short impulse radius, and one against it. Now, 
let us turn to the impulse action. Here we have the long- 
lever AW acting on a short one, A' X, which is a disad- 
vantage. Here, then, we ought to try and have a short 
lever acting on a long one, which would point to a short 
fork and a great impulse radius. Suppose AP, Fig. 14, 



28 THE LEVER ESCAPEMENT. 

is the length of fork, and AT is the impulse radius; here, 
then, we favor the impulse, and it is directly in accordance 
with the theory of the free vibration of the balance, for, 
as before stated, the longer the radius the smaller the an- 
gle. The action at P is also closer to the line of centers 
than it is at W, which is another advantage. 

We will notice that by employing a large impulse an- 
gle, and consequently a short radius, the intersection m 
of the two circles ii and cc is very safe, whereas, with 
the conditions reversed in favor of the impulse action, 
the intersection at k is more delicate. We have now seen 
enough to appreciate the fact that we favor one action at 
the expense of another. 

By having a lifting angle on pallet and tooth of 8y 2 °, 
a locking angle of ij4° y and a run of >2°, we will have 
an angular movement of the fork of 8j4-\- ij4+j4=ioj4°. 

Writers generally only consider the movement of the 
fork from drop to drop on the pallets, but we will be thor- 
oughly practical in the matter. With a total motion of the 
fork of ioy 2 ° (JAW, Fig. 15), one-half, or 5^° will be 
performed on each side of the line of centers. We are at 
liberty to choose any impulse angle which we may prefer; 
3 to 1 is a good proportion for an ordinary well-made watch. 
By employing it, the angle XA'Y would be equal to 31^2°. 
The radius A'X Fig. 16, is also of the same proportion, but 
the angle AA'X is greater because the fork angle WAA' 
is greater than the same angle in Fig. 15. We will notice 
that the intersection k is much smaller in Fig. 15 than in 
Fig. 16. The action in the latter begins much further from 
the line of centers than in the former and outlines an 
action which should not be made. 

To come back to the impulse angle, some might use 
a proportion of 3.5, 4 or even 5 to 1, while others for the 
finest of watches would only use 2.75 to 1. By having a 
total vibration of the balance of iy 2 turns, which is equal 
to 540 a fork angle of io° and a proportion of 2.75 for 



THE LEVER ESCAPEMENT. 2Q 

the impulse angle which would be equal to 10 X 2.75 = 
27.5 . The free vibration of the balance, or as this is 
called, "the supplemental arc," is equal to 540 — 27.5° = 
512.50 , while with a proportion of 5 to 1, making an 
impulse angle of 50 , it would be equal to 490 . To sum 
up, the finer the watch the lower the proportion, the closer 
the action to the line of centers, the smaller the friction. 
On account of leverage the more difficult the unlocking 
but the more energetic the impulse when it does occur. The 
velocity of the ruby pin at P; Fig. 14, is much greater 
than at W, consequently it will not be overtaken as soon 
by the fork as at W. The velocity of the fork at the latter 
point is greater than at P ; the intersection of it and cc is also 
not as great; therefore the lower the proportion the finer 
and more exact must the workmanship be. 

We will notice that the unlocking action has been over- 
ruled by the impulse. The only point so far in which 
the former has been favored is in the diminished action 
before the line of centers, as previously pointed out at P, 
Fig. 14. 

We will now consider the width of the ruby pin and 
to get a good insight into the question, we will study 
Fig. 17. A is the pallet center, A' the balance center, 
the line AA' being the line of centers; the angle WAA 
equals half the total motion of the fork, the other half, 
of course, taking place on the opposite side of the center 
line. WA is the center of the fork when it rests against 
the bank. The angle AA'X represents half the impulse 
angle; the other half, the same as with the fork, is struck 
on the other side of the center line. At the point of in- 
tersection of these angles we will draw cc from the pallet 
center A, which equals the acting length of the fork, and 
from the balance center we will draw ii, which equals 
the theoretical impulse radius; some writers use it as the 
real radius. The wider the ruby pin the greater will the 
latter be, which we will explain presently. ■ 



30 THE LEVER ESCAPEMENT. 

The ruby pin in entering the fork must have a certain 
amount of freedom for action, from I to i*4°- Should 
the watch receive a jar at the moment the guard point 
enters the crescent or passing hollow in the roller, the 
fork would fly against the ruby pin. It is important that the 
angular freedom between the fork and ruby pin at the 
moment it enters into the slot be less than the total lock- 
ing angle on the pallets. If we employ a locking angle 
of iy 2 ° and y 2 ° run, we would have a total lock on the 
pallets of 2°. By allowing i%° of freedom for the ruby 
pin at the moment the guard point enters the crescent, 
in case the fork should strike the face of the ruby pin, 
the pallets will still be locked J4° and the fork drawn back 
against the bankings through the draft angle. 

We will see what this shake amounts to for a given 
acting length of fork, which describes an arc of a circle, 
therefore the acting length is only the radius of that circle 
and must be multiplied by two in order to get the diameter. 
The acting length of fork=4»5 mm., what is the amount 
of shake when the ruby pin passes the acting corner? 
4.5X2X3.i4i6-^36o°=.o785Xi-25=.0992 mm. The shake 
of the ruby pin in the slot of the fork must be as slight 
as possible, consistent with perfect freedom of action. It 
varies from %° to y 2 ° , according to length of fork and 
shape of ruby pin. A square ruby pin requires more shake 
than any other kind ; it enters the fork and receives the im- 
pulse in a diagonal direction on the jewel, in which posi- 
tion it is illustrated at Z, Fig. 20. This ruby pin acts 
on a knife edge, but for all that the engaging friction 
during the unlocking action is considerable. 

Our reasoning tells us it matters not if a ruby pin be 
wide or narrow, it must have the same freedom in passing 
the acting edge of the fork, therefore, to have the impulse 
radius on the point of intersection of A'X with AW, Fig. 
17, we would require a very narrow ruby pin. With i° 
of freedom at the edge, and y 2 ° in the slot, we could only 



THE LEVER ESCAPEMENT. 



31 



have a ruby pin of a width of 1 J/2 . Applying it to the 
preceding example it would only have an actual width 
of .0785 X 1. 5==. 1 178 mm., or the size of an ordinary bal- 
ance pivot. At n, Fig. 17, we illustrate such a ruby pin; 
the theoretical and real impulse radius coincide with one 
another. The intersection of the circle ii and cc is very 
slight, while the friction in unlocking begins within i° of 
half the total movement of the fork from the line of 
centers; to illustrate, if the angular motion is ii° the ruby 



\/> 








Fig. 17. 



Fig. 18. 



Fig. 19. 



Fig. 20. 



pin under discussion will begin action 4^2° before the line 
of centers, being an engaging, or "uphill" friction of con- 
siderable magnitude. 

The intersection with the fork is also much less than 
with the wider ruby pin, making the impulse action very 
delicate. On the other hand the widest ruby pin for which 
there is any occasion is one beginning the unlocking action 
on the line of centers, Fig. 17; this entails a width of slot 
equal to the angular motion of the fork. We see here the 
advantage of a wide ruby pin over a harrow one in the 
unlocking action. Let us now examine the question from 
the standpoint of the impulse action. 



32 THE LEVER ESCAPEMENT. 

Fig. 1 8 illustrates the moment the impulse is transmit- 
ted ; the fork has been moved in the direction of the arrow 
by the ruby pin ; the escapement has been unlocked and the 
opposite side of the slot has just struck the ruby pin. The 
exact position in which the impulse is transmitted varies 
with the locking angle, the width of ruby pin, its shake 
in the slot, the length of fork, its weight, and the velocity 
of the ruby pin, which is determined by the vibrations 
of the balance and the impulse radius. 

In an escapement with a total lock of i}i° and i*4 of 
shake in the slot, theoretically, the impulse would be trans- 
mitted 2° from the bankings. The narrow ruby pin n 
receives the impulse on the line v, which is closer to the 
line of centers than the line u, on which the large ruby pin 
receives the impulse. Here then we have an advantage of 
the narrow ruby pin over a wide one; with a wider ruby 
pin the balance is also more liable to rebank when it takes 
a long vibration. Also on account of the greater ano-le 
at which the ruby pin stands to the slot when the impulse 
takes place, the drop of the fork against the jewel will 
amount to more than its shake in the slot (which is meas- 
ured when standing on the line of centers). On this ac- 
count some watches have slots dovetailed in form, being 
wider at the bottom, others have ruby pins of this form. 
They require very exact execution ; we think we can do 
without them by judiciously selecting a width of ruby pin 
between the two extremes. We would choose a ruby pin 
of a width equal to half the angular motion of the fork. 
There is an ingenious arrangement of fork and roller which 
aims to, and partially does, overcome the difficulty of choos- 
ing between a wide and narrow ruby pin, it is known as the 
"Savage pin roller escapement. We intend to describe it 
later. 

If the face of the ruby pin were planted on the theoret- 
ical impulse radius ii, Fig. 19, the impulse would end in a 
butting action as shown ; hence the great importance of dis- 



THE LEVER ESCAPEMENT. 



33 



tinguishing between the theoretical and real impulse radius 
and establishing a reliable data from which to work. We 
feel that these actions have never been properly and thor- 
oughly treated in simple language ; we have tried to make 
them plain so that anyone can comprehend them with a 
little study. 

Three good forms of ruby pins are the triangular, the 
oval and the flat faced; for ordinary work the latter is as 
good as any, but for fine work the triangular pin with the 
corners slightly rounded off is preferable. 




\n 



G 



Fig. 21. 




© 






\ G 



-- < 



Fig. 23. 



:o 



Fig. 22. 



English watches are met with having a cylindrical or 
round ruby pin. Such a pin should never be put into a 
watch. The law of the parallelogram of forces is completely 
ignored by using such a pin; the friction during the un- 
locking and impulse actions is too severe, as it is, without 
the addition of so unmechanical an arrangement. Fig. 21 
illustrated the action of a round ruby pin; ii is the path 
of the ruby pin; cc that of the acting length of the fork. 
It is shown at the moment the impulse is transmitted. It 
will be seen that the impact takes place below the center of 
the ruby pin, whereas it should take place at the center, 
as the motion of the fork is upivards and that of the ruby 



34 



THE LEVER ESCAPEMENT. 



pin downwards until the line of the centers has been reached. 
The same rule applies to the flat-faced pin and it is impor- 
tant that the right quantity be ground off. We find that 
3/7 is approximately the amount which should be ground 
away. Fig. 22 illustrates the fork standing against the 
bank. The ruby pin touches the side of the slot but has 
not as yet begun to act; ri is the real impulse circle for 
which we allow i~y° of freedom at the acting edge of 
the fork ; the face of the ruby pin is therefore on this line. 
The next thing to do is to find the center of the pin. From 




the side n of the slot we construct the right angle n t; from 
n, we transmit y* the width of the pin, and plant the center 
x on the line n t. We can have the center of the pin slightly 
below this line, but in no case above it; but if we put it 
below, the pin will be thinner and therefore more easily 
broken. 

The Safety Action. Although this action is separate 
from the impulse and unlocking actions, it is still very 
closely connected with them, much more so in the single 
than in the double roller escapement. If we were to place 



THE LEVER ESCAPEMENT. 35 

the ruby pin at X, Fig. 14, we could have a much smaller 
roller than by placing it at P. With the small roller the 
safety action is more secure, as the intersection at m is 
greater than at k. It is not as liable to "butt" and the fric- 
tion is less when the guard point is thrown against the 
small roller. Suppose we take two rollers, one with a diam- 
eter of 2.5 mm., the other just twice this amount, of 5 
mm. By having the guard radius and pressure the same in 
each case, if the guard point touched the larger roller it 
would not only have twice, but four times more effect 
than on the smaller one. We will notice that the smaller 
the impulse angle the larger the roller, because the ruby 
pin is necessarily placed farther from the center. The po- 
sition of the ruby pin should, therefore, govern the size of 
the roller, which should be as small as possible. There 
should only be enough metal left between the circumference 
of the roller and the face of the jewel to allow for a cres- 
cent or passing hollow of sufficient depth and an efficient set- 
ting for the jewel. For this reason, as well as securing the 
correct impulse radius and therefore angle, when replacing 
the ruby pin, and having it set securely and mechanically^ 
in the roller, it is necessary that the pin and the hole in 
the roller be of the same form and a good fit. Fig. 23 
illustrates the difference in size of rollers. In the smaller 
one the conditions imposed are satisfied, while in the larger 
one they are not. In the single roller the safety action is 
at the mercy of the impulse and pallet angles. We have 
noticed that in order to favor the impulse we require a 
large roller, and for the safety action a small one, therefore 
escapements made on fine principles are supplied with two 
rollers, one for each action. 

It may be well to say that in our opinion a proportion 
between the fork and impulse angles in io° pallets of 3 
or 3^ to 1, depending upon the size of the escapement, 
is the lowest which should be made in single roller. We 
have seen them in proportions of 2 to 1 in single roller — 



36 



THE LEVER ESCAPEMENT. 



a scientific principle foolishly applied — resulting in an ac- 
tion entirely unsatisfactory. 

When the guard point is pressed against the roller the 
escape tooth must still rest on the locking face of the pal- 
let; if the total lock is 2°, by allowing i%° freedom for 
the guard point between the bank and the roller the es- 
capement will still be locked 24°. How much this shake 
actually amounts to depends upon the guard radius. Sup- 
pose this to be 4 mm, then the freedom would equal 
4 X 2 X 3-Hi6 — 360 X 1.25 = .0873 mm. 





Fig. 24. 



Fig. 25. 



The Crescent in the roller must be large and deep 
enough so it will be impossible for the guard point to 
touch in or on the corners of it; at the same time it must 
not be too large, as it would necessitate a longer horn on 
the fork than is necessary. 

Fig. 24 shows the slot n of the fork standing at the bank. 
The ruby pin touches it, but has not as yet acted on it; 
j ^ illustrates a single roller, while S2 illustrates the safety 
roller for a double roller escapement. In order to find the 
dimensions of the crescent in the single roller we must 
proceed as follows : WA is in the center of the fork when 
it rests against the bank, and is, therefore, one of the sides 
of the fork angle, and is drawn from the pallet center; 
V A W is an angle of i%°, which equals the freedom 



THE LEVER ESCAPEMENT. 37 

between the guard point and the roller ; g g represents the 
path of the guard pin u for the single roller, and is drawn at 
the intersection of VA with the roller A' A2 is a line drawn 
from the balance center through that of the ruby pin, and 
therefore also passes through the center of the crescent. 
By planting a compass on this line, where it cuts the peri- 
phery of the roller, and locating the point of intersection of 
VA with the roller, will give us one-half the crescent, the 
remaining half being transferred to the opposite side of 
the line A' A2. We will notice that the guard point has 
entered the crescent i%° before the fork begins to move. 

The angle of opening for the crescent in the double roller 
escapement is greater than in the single, because it is placed 
closer to the balance center, and the guard point or dart 
further from the pallet center, causing a greater intersec- 
tion; also the velocity of the guard point has increased, 
while that of the safety roller has decreased. Fig. 24, at ff, 
shows the path of the dart h, which also has i%° freedom 
between bank and roller. From the balance center we draw 
A'd touching the center or point of the dart; from this 
point we construct at 5 angle b A' d. This is to ensure 
sufficient freedom for the dart when entering the crescent. 
We plant a compass on the point of intersection of A' A2 
with the safety roller, S2, and locating the point where A'& 
intersects it, have found one-half the opening for the 
crescent, the remaining half being constructed on the op- 
posite side of the line A' A2. 

The Horn on the fork belongs to the safety action : 
more horn is required with the double than with the 
single roller, on account of the greater angle of opening 
for the crescent. 

The horn should be of such a length that when the 
crescent has passed the guard point, the end of the horn 
should point to at least the center of the ruby pin. 

The dotted circle, s s, Fig. 25, represents a single roller. 
It will be noticed that the corner of the crescent has passed 



38 THE LEVER ESCAPEMENT. 

the guard pin u by a considerable angle, and although this 
is so, in case of an accident the acting edge T>f the fork 
would come in contact with the ruby pin; this proves that 
a well made single roller escapement really requires but 
little horn, only enough to ensure the safe entry of the ruby 
pin in case the guard point at that moment be thrown against 
the roller. We will now examine the question from the 
standpoint of the double roller; S2, Fig. 25, is the safety 
roller ; the corner of the crescent has safely passed the dart 
h ; the centers of the ruby pin and of the crescent being 
on the line A' A2, we plant the compass on the pallet cen- 
ter and the center of the face of the ruby pin and draw k k, 
which will be the path described by the horn. The end of 
the horn is therefore planted upon it from 1^2° to \}\° 
from the ruby pin; this freedom at the end of the horn is 
therefore from %° to j4° more than we allow for the 
guard point ; it depends upon the size of the escapement and 
locking angles which we would choose. It must in any 
case be less than the lock on the pallets, so that the fork 
will be drawn back against the bank in case the horn be 
thrown against the ruby pin. 

When treating on the width of the ruby pin, we men- 
tioned the Savage pin roller escapement, which we illus- 
trate in Figs. 26 and 27. This ingenious arrangement was 
designed with the view of combining the advantages of both 
wide and narrow pins and at the same time without any of 
their disadvantages. 

In Fig. 26 w T e show the unlocking pins u beginning 
their action on the line of centers — the best possible point 
— in unlocking the escapement. These pins were made of 
gold in all which we examined, although it is recorded that 
wide ruby pins and ruby rollers have been used in this es- 
capement, which would be preferable. 

The functions of the two pins in the roller are simply 
to unlock the escapement; the impulse is not transmitted 
to them as is the case in the ordinary fork and roller 



THE LEVER ESCAPEMENT. 



39 



action. In this action the guard pin i also acts as the im- 
pulse pin. We will notice that the passing hollow in this 
roller is a rectangular slot the same as in .the ordinary 
fork. When the escapement is being unlocked the guard 
pin i enters the hollow and when the escape tooth comes 
into contact with the lifting plane of the pallet the pin f, 
Fig. 27, transmits the impulse to the roller. 

The impulse is transmitted closer to the line of centers 
than could be done with any ruby pin. If the pin i were 




Fig. 26. 



Fig. 28. 



wider the impulse would be transmitted still closer to the 
line of centers, but the intersection of it with the roller 
would be less. It is very delicate as it is, therefore from 
a practical standpoint it ought to be made thin but con- 
sistent with solidity. If the pin is anyway large, it should 
be flattened on the sides, otherwise the friction would be 
similar to that of the round ruby pin. It would also be 
preferable (on account of the pin i being very easily bent) 



4° THE LEVER ESCAPEMENT. 

to make the impulse piece narrow but of such a length that 
it could be screwed to the fork, the same as the dart in the 
double roller. The impulse radius is also the radius of the 
roller, because the impulse is transmitted to the roller itself; 
for this reason the latter is smaller in this action than in 
the ordinary one having the same angles ; also a shorter 
lever is in contact with a longer one in the unlocking than 
in ordinary action of the same angles* but for all this the 
pins u u should be pitched close to the edge of the roller, 
as the angular connection of the balance with the escape- 
ment would be increased during the unlocking action. This 
escapement being very delicate requires a 12° pallet angle 
and a proportion between impulse and pallet angles of not 
less than 3 to 1, which would mean an impulse angle of 36° ; 
this, together with the first rate workmanship required 
are two of the reasons why this action is not often met with. 

George Savage, of London, England, invented this 
action. He was a watchmaker who, in the early part of 
this century, did much to perfect the lever escapement by 
good work and nice proportion, besides inventing the two 
pin variety. He spent the early part of his life in Clerk- 
enwell, but in his old days emigrated to Canada, and 
founded a flourishing retail business in Montreal, where 
he died. Some of George Savage's descendants are still 
engaged at the trade in Canada at the present day. 

The correct delineation of the lever escapement is a 
very important matter. We illustrate one which is so de- 
lineated that it can be practically produced. We have not 
noticed a draft of the lever escapement, especially with equi- 
distant pallets and club teeth, which would act correctly 
in a watch. 

We have been aggressive in our work and have some- 
times found theories propounded and elongated which of 
themselves were not right; this may have something to 
do with it, that we so often hear workmen say, "Theory 
is no use, because if you work according to it your ma- 



THE LEVER ESCAPEMENT. 41 

chine will not run." We say, "No, sir, if your theory 
is not right in itself, then your work will certainly not 
be correct; but if your theory be correct then your work 
must be correct. Why? it simply cannot be otherwise/' We 
will give it another name ; let us' say, apply sense, reason, 
thought, experience and study to your work, and what have 
you done ? You have simply applied theory. 

A theorem is a proposition to be proved, not being 
able to prove it, we must simply change it according as 
our experience dictates, this is precisely what we have 
done with the escapement after having followed the de- 
ductions of recognized authorities with the result that we 
can now illustrate an escapement which has been thoroughly 
subjected to an impartial analysis in every respect, and 
which is theoretically and practically correct. 

We will not only give instructions for drafting the 
escapement now under consideration, but will also make 
explanations how to draft it in different positions, also in 
circular pallet and single roller. We are convinced that 
by so doing we will do a service to many, we also wish 
to avoid what we may call "the stereotyped" process, that 
is, one which may be acquired by heart, but introduce any 
changes and perplexity is the result. It is really not a 
difficult matter to draft escapements in different positions, 
as an example will show. 

Before making a draft we must know exactly what we 
wish to produce. It is well in drafting escapements to 
make them as large as possible, say thirty to forty times 
larger than in the watch, in the present case the size is im- 
material, but we must have specifications for the proportions 
of the angles. Our draft is to be the most difficult sub- 
ject in lever escapements; it is to be represented just as 
if it were working in a watch; it is to represent a good 
and reliable action in every respect, one which can be ap- 
plied without special difficulty to a good watch, and* is to be 
-"up to date" in every particular and to contain the ma- 



42 THE LEVER ESCAPEMENT. 

jority of the best points and conclusions reached in our 
analysis. 

Specifications for Lever Escapement: The pallets are 
to te equidistant; the wheel teeth of the "club" form; 
there are to be two rollers; wheel, pallet, and balance cen- 
ters are to be in straight line. The lock is to be i%°, the 
run %°, making a total lock of 1^4°; the movement of 
pallets from drop to drop is to> be io°, while the fork is 
to move through io^° from bank to bank; the lift on the 
wheel teeth is to be 3 , while the remainder is to be the lift 
on the pallets as follows: io^4 — ( I M+3)=5/^° fc> r lift of 
pallets. 

The wheel is to have 15 teeth, with pallets spanning 3 
teeth or 2^2 spaces, making the angle from lock to lock 
=36o-f-i 5X2^=60°, the interval from tooth to tooth is 
36CK-15— 24 ; divided by 2 pallets=: 24^2=1 2 for width 
of tooth, pallet and drop ; drop is to be ij£°, the tooth is to be 
24 the width of the pallet, making a tooth of a width of 
AY* and a pallet of 6°. 

The draw is to be 12 on each pallet, while the lock- 
ing faces of the teeth are to incline 24 . The acting length 
of fork is to be equal to the distance of centers of scape 
wheel and pallets ; the impulse angle is to be 28 ° ; freedom 
from dart and safety, roller is to be ij4°, and for dart and 
corner of crescent 5 ; freedom for ruby pin and acting edge 
of fork is to be i/i° ; width of slot is to be ]/* the total 
motion, or io^-^- 2 =5%° ; shake of ruby pin in slot=j4°, 
leaving 5% — 14=47/3° for width of ruby pin. 

Radius of safety roller to be 4/7 of the theoretical im- 
pulse radius. The length of horn is to be such that the 
end would point at least to the center of the ruby pin 
when the edge of "the crescent passes the dart; space be- 
tween the end of horn and ruby pin is to be ij^°. 

It is well to know that the angles for width of teeth, 
pallets and drop are measured from the wheel center, while 
the lifting and locking angles are struck from the pallet 



THE LEVER ESCAPEMENT. 43 

center, the draw from the locking corners of the pallets, 
and the inclination of the teeth from the locking edge. 

In the fork and roller action, the angle of motion, the 
width of slot, the ruby pin and its shake, the freedom 
between dart and roller, of ruby pin with acting edge of fork 
and end of horn are all measured from the pallet center, 
while the impulse angle and the crescent are measured from 
the balance center. A sensible drawing board measures 
17x24 inches, we also require a set of good drawing in- 
struments, the finer the instruments the better; pay special 
attention to the compasses, pens and protractor; add to 
this a straight ruler and set square. 

The best all-round drawing paper, both for India ink 
and colored work has a rough surface;, it must be fas- 
tened firmly and evenly to the board by means of thumb 
tacks ; the lines must be light and made with a hard pencil. 
Use Higgins' India ink, which dries rapidly. 

We will begin by drawing the center line A'AB; use 
the point B for the escape center; place the compass on 
it and strike G H, the primitive or geometrical circle of 
the escape wheel; set the center of the protractor at B 
and mark off an angle of 30 on each side of the line of 
centers ; this will give us the angles ABE and A B F to- 
gether, forming the angle F B E of 6o°, which represents 
from lock to lock of the pallets. Since the chord of the 
angle of 6d° is equal to the radius of the circle, this gives 
us an easy means of verifying this angle by placing the 
compass at the points of intersection of F B and E B with 
the primitive circle G H ; this distance must be equal to the 
radius of the circle. At these points we will construct right 
angles to E B and F B, thus forming the tangents C A and 
D A to the primitive circle G H. These tangents meet. on 
the line of centers at A, which will be the pallet center. 
Place the compass at A and draw the locking* circle M N at 
the points of intersection of E B and F B with the primitive 
circle G H. The locking edges of the pihkts will always 



44 



THE LEVER ESCAPEMENT. 




#U^" 



THIS IS 

GOVERNMENT PROPERTY 

FOR OFFICIAL USE OMIT 
ACCOUNTED FOR IN ACCOMANCE ¥NI« M. Mil. 



THE LEVER ESCAPEMENT. 45 

stand on this circle no matter in what relation the pallets 
stand to the wheel. Place the center of the protractor at 
B and draw the angle of width of pallets of 6° ; I B E being 
for the engaging and J B F for the disengaging pallet. In 
the equidistant pallet I B is drawn on the side towards the 
center, while J B is drawn further from the center. If we 
were drawing a circular pallet, one-half the width of pallets 
would be placed on each side of E B and F B. At the points 
of intersection of I B and J B with the primitive circle G H 
we draw the path O for the discharging edge of the engag- 
ing and P for that of the disengaging pallet. The total 
lock being i}i°, we construct V A at this angle from C A ; 
the point of intersection of V A with the locking circle 
M N, is the position of the locking corner of the engaging 
pallet. The pallet having 12° draw when locked we place 
the center of the protractor on this corner and draw the 
angle Q M E. QM will be the locking face of the engag- 
ing pallet. If the face of the pallet were on the line E B 
there would be no draw, and if placed to the opposite side 
of E B the tooth would repel the pallet, forming what is 
known as the repellant escapement. 

Having shown how to delineate the locking face of the 
engaging pallet when locked, we will now consider how 
to draft both it and the disengaging pallet in correct posi- 
tions when unlocked; to do so we direct our attention 
until further notice to Fig. 28. The locking faces Q M of 
the engaging and S N of the disengaging pallets are shown 
in dotted lines when locked. We must now consider the re- 
lation which the locking faces will bear to E B in the en- 
gaging, and to F B in the disengaging pallets when un- 
locked. This is a question of some importance ; it is easy 
enough to represent the 12° from the 30° angles when 
locked; we must be certain that^hs* would occupy ex- 
actly that position and yet shoV*ri<mr unlocked ; we shall 
take pains t<gKfe> so. In due tirJreffev^hall^show that these 
is no appreciable loss of lift on tMfe &i£&$£$gfysitet m the 



46 THE LEVER ESCAPEMENT. 

escapement illustrated; the angle T A V therefore shows 
the total lift; we have not shown the corresponding angles 
on the disengaging side because the angles are somewhat 
different, but the total lift is still the same. G H represents 
the primitive circle of the escape wheel, and X Z that of 
the real, while M N represents the circular course which the 
locking corners of the pallets take in an equidistant escape- 
ment. At a convenient position we will construct the circle 
C C D from the pallet center A. Notice the points e and c, 




i 

V 

Fig. 28. 



where V A and T A intersect this circle; the space between 
e and c represents the extent of. the motion of the pal- 
lets at this particular distance from the center A; this be- 
ing so, then let us apply it to the engaging pallet At the 
point of intersection of the dotted line Q M (which is an 
extended line on which the face of the pallet lies when 
locked), with the circle C C D, we will plant our dividers 
and transfer e c to n. By setting our dividers on M and 
transferring to n M', we will obtain the location of Q' M', 
the locking face when unlocked. Let us now turn our at- 



THE LEVER ESCAPEMENT. 47 

tention to the disengaging pallet. The dotted line S N rep- 
resents the location of the locking face of the disengaging 
pallet when locked at an angle of 12° from F B. At the in- 
tersection of S N with the circle C C D we obtain the point 
/. The motion of the two pallets being equal, we transfer 
the distance e c with the dividers from / and obtain the 
point /. By setting the dividers on / N and transferring to 
/ N' we draw the line S' N' on which the locking face of the 
disengaging pallet will be located when unlocked. It will 
be perfectly clear to anyone that through these means we 
can correctly represent the pallets in any desired position. 

We will notice that the face Q' M' of the engaging pal- 
let when unlocked stands at a greater angle to E B than it 
did when locked, while the opposite is the case on the dis- 
engaging pallet, in which the angle S' N' F is much less 
than S N F. This shows that the deeper the engaging pal- 
let locks, the lighter will the draw be, while the opposite 
holds good with the disengaging pallet ; also, that the draw 
increases during the unlocking of the engaging, and de- 
creases during the unlocking of the disengaging pallet. 
These points show that the draw should be measured with 
the fork standing against the bank, not when the locking 
corner of the pallet stands on the primitive circle, as is so 
often done. The recoil of the wheel (which determines 
the draw), is illustrated by the difference between the lock- 
ing circle M N and the face Q M for the engaging, and* S N 
for the disengaging pallet, and along the acting surface it 
is alike on each pallet, showing that the draft angle should 
be the same on each pallet. 

A number of years ago we constructed the escapement 
model which we herewith illustrate. All the parts are 
adjustable; the pallets can be moved in any direction, the 
draft angles can be changed at will. Through this model 
we can practically demonstrate the points of which we have 
spoken. Such a model can be made by workmen after 
studying these papers. 



48 



THE LEVER ESCAPEMENT. 



In both the equidistant and circular pallets the locking 
face S N of the disengaging pallet deviates more from 
the locking circle M N than does the locking face Q M 




of the engaging pallet, as will" be seen in the diagram. This 
is because the draft angle is struck from E B which deviates 
from the locking circle in such a manner, that if the face 
of a pallet were planted on it and locked deep enough to 






THE LEVER ESCAPEMENT. 49 

show it, the wheel would actually repel the pallet, whereas 
with the disengaging pallet if it were planted on F B, it 
would actually produce draw if locked very deep; this is 
on account of the natural deviation of the 30 lines from 
the locking circle. This difference is more pronounced in 
the circular than in the equidistant pallet, because in the for- 
mer we have two locking circles, Ihe larger one being for 
the engaging pallet, and as an arc of a large circle does not 
deviate as much from a straight line as does that of a smaller 
circle, it will be easily understood that the natural differ- 
ence before spoken of is only enhanced thereby. For 
this reason in order to produce an actual draw of 12 , 
the engaging pallet may be set at a slightly greater an- 
gle from E B in the circular escapement; the amount de- 
pends upon the width of the pallets ; the requirements 
are that the recoil of the wheel will be the same on 
each pallet. We must, however, repeat that one of the 
most important points is to measure the draw when the 
fork stands against the bank, thereby increasing the draw 
on the engaging and decreasing that of the disengaging 
pallet during the unlocking action, thus naturally balancing 
one fault with another. 

We will again proceed with the delineation of the 
escapement here illustrated. After having drawn the lock- 
ing face Q M, we draw the angle of width of teeth of 
4/4°, by planting the protractor on the escape center B. 
We measure the angle EBK, from the locking face of the 
pallet; the line E B does not touch the locking face of the 
pallet at the present time of contact with the tooth, there- 
fore a line must be drawn from- the point of contact to the 
center B. We did so in our drawing but do not illustrate it, 
as in a reduced engraving of this kind it would be too 
close to E B. and would only cause confusion. We will 
now draw in the lifting angle of 3 for the tooth. From the 
tangent C A we draw T A at the required angle; at the 
point of intersection of T A with the 30 line E B we have 



50 THE LEVER ESCAPEMENT. 

the real circumference of the escape wheel. It will only be 
necessary to connect the locking edge of the tooth with the 
line K B, where the real or outer circle intersects it. It 
must be drawn in the same manner in the circular escape- 
ment; if the tooth were drawn up to the intersection of 
K B with T A, the lift would be too great, as that point 
is further from the center A than the points of contact are. 
If the real or outer circle of the wheel intersects both 
the locking circle M N and the path O of the discharging 
edge at the points where T A intersects them, then there 
will be no loss of lift on the engaging pallet. This is pre- 
cisely how it is in the diagram ; but if there is any devia- 
tion, then the angle of loss must be measured on the real 
diameter of the wheel and not on the primitive, as is usually 
done, as the real diameter of the wheel, or in other words 
the heel of the tooth, forms the last point of contact. With 
a wider tooth and a greater lifting angle there will even be 
a gain of lift on the engaging pallet; the pallet in such 
a case would actually require a smaller lifting angle, ac- 
cording to the amount of gain. We gave full directions for 
measuring the loss when describing its effects in Fig. 8. 
Whatever the loss amounts to, it is added to the lifting 
plane of the pallet. In the diagram under discussion there 
is no loss, consequently the lifting angle on the pallet is to be 
5/4°. From V A we draw V A at the required angle; the 
point of intersection of V A with the path O will be the 
discharging edge O. It will now only be necessary to con- 
nect the locking corner M with it, and we have the lift- 
ing plane of the pallet; the discharging side of the pallet 
is then drawn parallel to the locking face and made a 
suitable length. We will now draw the locking edges of the 
tooth by placing the center of the protractor on the lock- 
ing edge M and construct the angle B M M' of 24 
and draw a circle from the scape center B, to which the 
line M M' will be a tangent. We will utilize this cir- 
cle in drawing in the faces of the other teeth after hav- 



THE LEVER ESCAPEMENT. 5 1 

ing spaced them off 24 apart, by simply putting a ruler 
on the locking edges and on the periphery of the circle. 

We now construct W A as a tangent to the outer cir- 
cle of the wheel, thus forming the lifting angle D A W 
of 3 for the teeth; this corresponds to the angle T A C 
on the engaging side. W' A touches the outer circle of 
the wheel at the intersection of F B with it. We will 
notice that there is considerable deviation of W' A from 
the circle at the intersection of J B with it. At the inter- 
secting of this point we draw U A; the angle U A W' is 
the loss of lift. This angle must be added to the lifting 
angle of the pallets ; we see that in this action there 
is no loss on the engaging pallet, but on the disengaging 
the loss amounts to approximately %° in the action illus- 
trated. As we have allowed %° of run for the pallets, 
the discharging edge P is removed at this angle from U 
A; we do not illustrate it, as the lines would cause con- 
fusion being so close together. The lifting angle on the 
pallet is measured from the point P and amounts to 5^4° 
+ the angle of the- loss; the angle W A U embraces the 
above angles besides j4° for run - If the locks are equal 
on each pallet, it proves that the lifts are also equal. This 
gives us a practical method of proving the correctness of 
the drawing; to do so, place the dividers on the locking 
circle M N at the* intersection of T A and V A with it, 
as this is* the extent of motion ; transfer this measurement 
to N, if the actual lift is the same on each pallet, the divid- 
ers will locate the point which the locking corner N will 
occupy when locked; this, in the present case, will be at 
an angle of i}i° below the tangent D A. By this sim- 
ple method, the correctness of our proposition that the loss 
of lift should be measurecf from the outside cifcle . of 
the wheel, can be proven. We often see the loss meas- 
ured for the engaging pallet on the primitive circumfer- 
ence G H, and on the real circumference for the disen- 
gaging; if one is right then the other must be wrong, as 



52 THE LEVER ESCAPEMENT. 

there is a noticeable deviation of the tangent C A from the 
primitive circle G H at the intersection of the locking circle 
M N ; had we added this amount to the lifting angle 
V A V of the engaging pallet, the result would have been 
that the discharging edge O would be over i° below its 
present location, thus showing that by the time the lift on. the 
engaging pallet had been completed, the locking corner N 
of the disengaging pallet would be locked at an angle of 
2^4° instead of only i^°. Many watches contain pre- 
cisely this fault. If we wish to make a draft showing the 
pallets at any desired position, at the center of motion for 
instance, with the fork standing on the line of centers, we 
would proceed in the following manner : io^4 ° being the 
total motion, one-half would equal 5^°; as the total lock 
equals i}i°, we deduct this amount from it which 
leaves 5^ — iM — 3H C \ which is the angle at which the 
locking corner M should be shown above the tangent C A. 
Now let us see where the locking corner N should stand; 
M having moved up 5^8°, therefore N moved down by 
that amount, the lift on the pallet being 5^° and on the 
tooth 3 (which is added to the tangent D A), it follows that 
N should stand 5^ + 3 — sV& ~ 3H° above D A. We can 
prove it by the lock, namely: ^H° + i$£ = sH°y hsdi the 
remaining motion. This shows how simple it is to draft 
pallets in various positions, remembering always to use the 
tangents to~ the primitive circle as measuring points. We 
have fully explained how to draw in the draft angle on the 
pallets when unlocked, and do not require to repeat it, except 
to say, that most authorities draw a tangent R N to the 
locking circle M N, forming in other words, the right angle 
R N A, then construct an angle of 12 from R N. We have 
drawn ours in by our own method, which is the correct one. 
While we here illustrate SNR at an angle of 12° it is in 
reality less than that amount ; had we constructed S N at an 
angle of 12 from R N, then the draw w r ould be 12 from 
F B, when the primitive circumference of the wheel is 



THE LEVER ESCAPEMENT. 53 

reached, but more than 12° when the fork is against the 
bank. 

The space between the discharging edge P and the heel 
of the tooth forms the angle of drop JBI of i^°; the 
definition for drop is that it is the freedom for wheel and 
pallet. This is not, strictly speaking, perfectly correct, as, 
during the unlocking action there will be a recoil of the 
wheel to the extent of the draft angle ; the heel of the tooth 
will therefore approach the edge P, and the discharging side 
of the pallet approaches the tooth, as only the discharging 
edge moves on the path P. 

A good length for the teeth is i/io the diameter of the 
wheel, measured from the primitive diameter and from the 
locking edge of the tooth. 

The backs of the teeth are hollowed out so as not to 
interfere with the pallets, and are given a nice form; like- 
wise the rim and arms are drawn in as light and as neat as 
possible, consistent with strength. 

Having explained the delineation of the wheel and pallet 
action we will now turn our attention to that of the fork 
and roller. We tried to explain these actions in such a man- 
ner that by the time we came to delineate them no difficulty 
would be found, as in our analysis we discussed the subject 
sufficiently to enable any one of ordinary intelligence to 
obtain a correct knowledge of them. The fork and roller 
action in straight line, right, or any ether angle is delineated 
after the methods- we are about to give. 

We specified that the acting* length of fork was to be 
equal to the center distance of wheel and pallets ; this gives 
a fork of a fair length. 

Having drawn the line of centers A' A we will con- 
struct an angle equal to half the angular motion of the 
pallets ; the latter in the case under consideration being 
io^4 °, therefore SJ/s is spaced off on each side of the line 
of centers, forming the angles m A k of io 1 /^ . Placing 
our dividers on A B the center distance of 'scape wheel and 



54 THE LEVER ESCAPEMENT. 

pallets, we plant them on A and. construct c c; thus we will 
have the acting length of fork and its path. We saw in 
our analysis that the impulse* angle* should be as small as. 
possible. We will use one of 28 in our draft of the double 
roller; we might however remark that this angle should 
vary with the construction of the escapements- in- different 
watches ; if too small, the balance may be stopped when the 
escapement 'is locked, while if too great it can be stopped 
during the lift ; both these* defects- are to be avoided. The 
angles being respectively 10^ ° and 28 it follows, they are 
of the following proportions: 28 ° -:- 10.25 := 2.7316. The 
impulse radius therefore bears this relation (but in the in- 
verse ratio to the angles), to the acting length of fork. 

We will put it in the following proportion ; let Ac equal 
acting length of fork, and x the unknown quantity; 
28:10.25 ::Ac:x; the answer will be the theoretical im- 
pulse radius. Having found the required radius we plant 
one jaw of our measuring instrument on the point of inter- 
section of c c with ^AorwA and locate the other jaw on 
the line of centers; we thus obtain A' the balance center. 
Through the points of intersection 'before designated we will 
draft X A' and Y A' forming the impulse angle X A' Y of 
28 °. At the intersection of this angle with the fork angle 
k A' m, we draw i i from the center A ; this gives us the 
theoretical impulse circle. The total lock being i^° it 
follows that the angle described by the balance in unlock- 
ing = i^4 X 2.7316 == 4.788 . According to the specifica- 
tions the width of slot is to* be 5^° ; placing the center of the 
protractor on A we construct half of this angle on each side 
of k A, which passes through the center of the fork when it 
rests against the bank ; this gives us the angle ^ A n of S/^°- 
If the disengaging pallet were shown locked then m A would 
represent the center of the fork. The slot is to be made of 
sufficient depth so there will be no possibility of the ruby pin 
touching the bottom of it. The ruby pin is to have 1^4^ 
freedom in passing the acting edge of the fork ; from the 



THE LEVER ESCAPEMENT. 55 

center A we construct the angle t A n of i%° ; at the point 
of intersection of t A with c c the acting radius of the fork, 
we locate the real impulse radius and draw the arc ri ri 
which describes the path made by the face of the ruby pin. 
The ruby pin is to have %° of shake in the slot ; it will there- 
fore have a width of 4}i° ; this width is drawn in with the 
ruby pin imagined as standing over the line of centers and is 
then transferred to the position which the ruby pin is to 
occupy in the drawing. 

The radius of the safety roller was given as 4/7 of the 
theoretical impulse radius. They may be made of various 
proportions; thus 2 /z is often used. Remember that the 
smaller we make it, the less the friction during accidental 
contact with the guard pin, the greater must the passing 
hollow be and the horn of fork and guard point must be 
longer, which increases the weight of the fork. 

Having drawn in the safety roller, and having specified 
that the freedom between the dart and safety roller was to 
be i%°, the dart being in the center of the fork, conse- 
quently k A is the center of it; therefore we construct the 
angle &AX of i}i°. At the point of intersection of X A 
with the safety roller we draw the arc g g; this locates the 
point of the dart which we will now draw in. We will next 
draw d A' from the balance center and touching the point 
of the dart; we now construct b A' at an angle of 5 ° to it. 
This is to allow the necessary freedom for the dart when 
entering the crescent ; from A' we draw a line through the 
center of the ruby pin. We do not show it in the drawing, as 
it would be indiscernible, coming very close to A' X. This 
line will also pass through the center of the crescent. At the 
point of intersection of A' b with the safety roller we have 
one of the edges of the crescent. By placing our compass at 
the center of the crescent on the periphery of the roller and 
on the edge which we have just found, it follows that our 
compass will span the radius of the crescent. We now sweep 
the arc for the latter, thus also drawing in the remaining 



56 THE LEVER ESCAPEMENT. 

half of the crescent on the other side of A' X and bringing 
the crescent of sufficient depth that no possibility exists of 
the dart touching in or on the edges of it. We will now 
draw in the impulse roller and make it as light as possible 
consistent with strength. A hole is shown through the im- 
pulse roller to counterbalance the reduced weight at the 
crescent. When describing Fig. 24, we gave instructions 
for finding the dimensions of crescent and position of guard 
pin for the single roller. We will find the length of horn; 
to do so we must closely follow directions given for Fig. 25. 
In locating the end of the horn, we must find the location 
of the center of the crescent and ruby pin after the edge of 
the crescent has passed the dart. From the point of inter- 
section of A' b with the safety roller we transfer the radius 
of the crescent on the periphery of the safety roller towards 
the side against the bank, then draw a line from A' through 
the point so found. At point of intersection of this line 
with the real impulse circle r ir i we draw an arc radiating 
from the pallet center ; the end of the horn will be located on 
this arc. In our drawing the arc spoken of coincides with 
the dart radius g g. As before pointed out, we gave par- 
ticulars when treating on Fig. 25, therefore considered it 
unnecessary to further complicate the draft by the addition 
of all the constructional lines. We specified that the free- 
dom between ruby pin and end of horn was to be 1 ]/ 2 ° ; 
(these lines, which we do not show) are drawn from the 
pallet center. Having located the end of the horn on the 
side standing against the bank, we place the dividers on it 
and on the point of intersection of k A with g g — which in 
this case is on the point of the dart, — and transfer this meas- 
urement along g g which will locate the end of the horn on 
the opposite side. 

We have the acting edges of the fork on cc and have also 
found the position of the ends of the horns ; their curvature 
is drawn in the following manner : We place our com- 
passes on A and r i, spanning therefore the real impulse 



THE LEVER ESCAPEMENT. 57 

radius ; the compass is now set on the acting edge of the fork 
and an arc swept with it which is then to be intersected by 
another arc swept from the end of the horn, on the same 
side of the fork. At the point of intersection of the arcs the 
compass is planted and the curvature of the horn drawn in, 
the same operation is to be repeated with the other horn. 
We will now draw in the sides of the horn of such a form 
that should the watch rebank, the side of the ruby pin will 
squarely strike the fork. If the back of the ruby pin strikes 
the fork there will be a greater tendency of breaking it and 
injuring the pivots on account of acting like a wedge. The 
fork and pallets are now drawn in as lightly as possible and 
of such form as to admit of their being readily poised. The 
banks are to be drawn at equal distances from the line of 
centers. In delineating the fork and roller action in any 
desired position, it must be remembered that the points of 
location of the real impulse radius, the end of horn, the dart 
or guard pin and crescent, must all be obtained when stand- 
ing against the bank, and the arcs drawn which they de- 
scribe ; the parts are then located according to the angle at 
which they are removed from the banks. 

We think the instructions given are ample to enable any 
one to master the subject. We may add that when one 
becomes well acquainted with the escapement, many of the 
angles radiating from a common center, may be drawn in 
at once. We had intended describing the mechanical con- 
struction of the escapement, which does unmistakably present 
some difficulties on account of the small dimensions of the 
parts, but nevertheless it can be mechanically executed true 
to the principles enumerated. We have evolved a method 
of so producing them that young men in a comparatively 
short period have made them from their drafts (without 
automatic machinery) that their watches start off when run 
down the moment the crown is touched. Perhaps later on 
we will write up the subject. It is our intention of doing so, 
as we make use of such explanations in our regular work. 






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